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concentration of this certain component and relatively m a l l weights are used for the other components. Furthermore, instead of the least squares criterion, any other criterion can also be used in the procedure discussed above.An estimation problem with multipoint boundary value (3) in difference equations can also be solved by essentially the same approach. For example, it is frequently necessary to have a certain specified purity of a certain side stream. Since this side stream is located at a plate inside the column and not at the terminals, a multipoint boundary-value problem is formulated. Many other specifications of the conditions of a distillation column are possible ( 5 ) . As we shall see in later papers, the present approach has certain distinct advantages over the conventional procedures for some of the specifications.It should be emphasized that the problem formulated does not always have solution. For example, the specified purity of the end product must be within the capability of the specified column in order for a solution to exist. The estimation approach avoids this problem. This is because of the fact that the least squares criterion only demands a solution that is as near as possible to the desired one. ACKNOWLEDGMENTThe work was partially supported by National Science Foun-

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